1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statics problem involving moments and reaction forces

  1. Mar 14, 2015 #1
    1. The problem statement, all variables and given/known data

    upload_2015-3-14_19-48-32.png
    The right angle boom which supports the 230-kg cylinder is supported by three cables and a ball-and-socket joint at O attached to the vertical x-y surface. Determine the reactions at O and the cable tensions.
    2. Relevant equations
    M
    = r x F
    unit vector = (vector)/(magnitude of vector)
    weight = weight of hanging mass = 230*9.81 = 2256.3 N
    3. The attempt at a solution
    So far, I've gotten two of the reaction forces and two of the cable tensions. Using unit vectors, I was able to solve for the tension vectors:
    T_ac = <-.4745, .4745, -.7414>T_ac
    T_bd = <0, .7880, -.6156>T_bd
    T_be = <0, 0, -1>T_be

    Because the moment about an axis sums to zero:
    ΣM_x = 0
    0 = (weight of mass - .4745*T_ac - .7880*T_bd)*radius from axis
    T_ac = (1/.4745)(2256.3 - .7880*T_bd)

    ΣM_z = 0
    0 = (T_bd*.7880 - .5*weight)*radius from axis
    T_bd = 1431.66 N which goes to 1430 N (The homework site I'm using only allows three significant digits.)

    T_ac = (1/.4745)(2256.3 - .7880*T_bd)
    T_ac = 2377.56 N which goes to 2380 N

    Up until this point, all the forces were equidistant from the axis in question.

    Somewhere in here my numbers get messed up - the previous two tension forces are correct, but this one is wrong.

    ΣM_y = 0
    0 = T_ac*-.4745*2.5 - T_be*-1*1.9 - T_be*1.9 + .6156*1.9*T_bd
    T_be = (1/1.9)(T_ac*.4745*2.5 - .6156*1.9*T_bd)
    T_be = 606 N



    Solving for the reaction forces:
    ΣF_x = 0
    0 = T_ac*-.4745 + O_x
    O_x = 1130 N

    ΣF_y = 0
    0 = O_y + .4745*T_ac + T_bd*.7880 - weight
    O_y = 0 N

    These two reaction forces are correct, so if I'm doing something wrong up to this point, I'm making compensating errors. The next reaction force is incorrect, but it depends on T_be and since I know that number is wrong, even if my method here is correct, I won't be able to get the right answer.

    ΣF_z = 0
    0 = -.7414*T_ac - .6156*T_bd - T_be + O_z
    O_z = 3250 N


    I'm not sure what I'm doing wrong, but at this point I'd be happy to find any mistake!

    Thanks for your time!
     
  2. jcsd
  3. Mar 14, 2015 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Just giving you work a quick eyeball, TBD should have three non-zero components.

    Also, when determining the sign of the components of a vector TBD, for example, these are usually calculated (xD - xB, yD - yB, zD - zB). [note the order]
     
  4. Mar 14, 2015 #3
    I'm not quite sure I follow you. I calculated the unit vector for T_bd as follows:

    B: <1.9, 0, 2.5>
    D: <1.9, 3.2, 0>

    BD = D - B
    BD
    = <0, 3.2, -2.5>
    n_bd = <0, 3.2, -2.5> / (3.2^2 + 2.5^2)^.5
    T_bd = n_bd * T_bd
    T_bd = <0, .7880, -.6156>


    Am I messing up the initial values for B and D?
     
  5. Mar 15, 2015 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    No, it's my mistake here. I read the distance wrong from the diagram of the frame in the OP. :frown:
     
  6. Mar 15, 2015 #5

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    My calculations for T_ac and T_bd agree with yours. :smile:

    Why are you convinced that T_be is wrong?

    I agree with your calculation of T_be. What is O_z supposed to be if 3250 N is incorrect? :sorry:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted